most recent 30 from http://mathoverflow.net 2013-05-19T07:14:09Z http://mathoverflow.net/feeds/question/107996 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107996/examples-of-finitely-generated-elementary-amenable-groups-which-are-not-virtually Mustafa Gokhan Benli 2012-09-24T17:59:42Z 2012-09-26T15:45:02Z

<p>What are some examples of finitely generated (finitely presented) elementary amenable groups which are not virtually solvable? </p>

http://mathoverflow.net/questions/107996/examples-of-finitely-generated-elementary-amenable-groups-which-are-not-virtually/108173#108173 Yves Cornulier 2012-09-26T15:34:45Z 2012-09-26T15:45:02Z

<p>Houghton groups are (non-split) extensions of the group of the finitely supported permutations of the integers by $\mathbf{Z}^d$ for $d\ge 2$ and are thus elementary amenable and not virtually solvable. They're finitely presented, as shown by K.Brown <a href="http://math.cornell.edu/~kbrown/scan/1987.0044.0045.pdf" rel="nofollow">here</a> (<i>Finiteness properties of groups</i>, JPAA 1987). They were introduced by Houghton as f.g. groups with coset spaces with <code>$2&lt;n&lt;\infty$</code> ends. </p>